Never underestimate the effectiveness of classical hand analysis methods. A good engineer can come up with a "back of the envelope" calculation for darned near anything within his field of expertise.
That said, you should always do at least a "sanity check" calculation on your FEA just to filter out any BC or load errors and to feel confident that you believe the results.
Think of it as hand tools vs. power tools. There is a lot of overlap between when each can be used but, sometimes you need to fine control and feedback of a hand tool and other times you need the brute force and speed of the power tool.
You don't hang picture frames with a nailgun and you don't go through a 4x8 sheet of plywood with a hand saw.
i can usually build and run an FEA model faster than I can find a textbook! Plus I have found most hand-calculation equations have been converted to web-based scripts which are easy to use as checks. Just do a google on what u want to find.
